Random Intercept, Random Slope

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TTP

Target Product Profile Decisions

Decision percentages when tau_LRV = tau_TV = 0.025

nk	NO-GO	Continue	GO
Slope, %: -10%
20	0.44	0.56	0.00
30	0.60	0.40	0.00
40	0.72	0.28	0.00
60	1.00
80	1.00
Slope, %: 10%
20	0.08	0.83	0.09
30	0.12	0.76	0.12
40	0.15	0.69	0.16
60	0.35	0.24	0.41
80	0.41	0.07	0.52
Slope, %: 20%
20	0.02	0.73	0.25
30	0.03	0.61	0.36
40	0.03	0.51	0.46
60	0.04	0.05	0.91
80	0.02	0.00	0.98
Slope, %: 30%
20	0.01	0.49	0.50
30	0.00	0.36	0.63
40	0.00	0.22	0.78
60		0.00	1.00
80			1.00
Slope, %: 40%
20	0.00	0.29	0.71
30	0.00	0.12	0.88
40		0.04	0.96
60			1.00
80			1.00

When theta_lrv = 0, theta_TV = 20, tau_LRV = tau_TV = 0.025.

Ranking

\(\psi_1\): Comparing Against Control

\(f(\psi_2)\): Comparing estimated confidence in top 2 regimens

\(\psi_3\): Posterior probability of ranking in top 2

Together

• TTP (high-low) and Mixed survival rates such that:
  • Regimen 1 (control): 5% relapse rate, reference log10(TTP) slope
  • Regimen 2 (sub-optimal regimen): 10% relapse rate, -10% relative log10(TTP) slope
  • Regimen 3 (minimal regimen): 5% relapse rate, 10% relative log10(TTP) slope
  • Regimen 4 (minimal regimen): 5% relapse rate, 35% relative log10(TTP) slope
  • Regimen 5 (desirable regimen): 2.5% relapse rate, 40% relative log10(TTP) slope

Stopping sub-optimal regimens

Stopping based on:

• TTP decision: NO-GO
• P(rank in top 2) < 60%
• Relapses >= 2

Slope	Stop relapse	Stop TPP	P(top 2) < 0.6	Stop relapse or TPP	Stop relapse or TPP or P(top 2) < 0.6
-10%	0.205	0.603	1.000	0.686	1
10%	0.232	0.112	0.977	0.317	1
20%	0.210	0.028	0.824	0.236	1

De-prioritizing sub-optimal regimens

De-prioritizing based on:

• TTP decision: NO-GO, Continue
• P(rank in top 2) < 60%
• Relapses >= 2

Slope	Stop relapse	Stop TPP	P(top 2) < 0.6	Stop relapse or TPP	Stop relapse or TPP or P(top 2) < 0.6
-10%	0.205	0.998	1.000	0.998	1
10%	0.232	0.875	0.977	0.902	1
20%	0.210	0.640	0.824	0.720	1

Desirable regimens

Slope	GO relapse	GO TPP	P(top 2) >= 0.6	GO relapse and TPP	GO relapse and TPP and P(top 2) >= 0.6
-10%	1.00	0.002	0.000	0.002	0.000
10%	1.00	0.123	0.014	0.123	0.123
20%	0.79	0.360	0.176	0.280	0.280

Single Example

Interim results from a single simulated phase 2B study with thirty partients per regimen. The target product profile (TPP) assumes \(\theta_{LRV} = 0, \theta_{TV} = 20, \tau_{LRV} = \tau_{TV} = 0.025\).

		Interim 1
Regimen	Duration	No. patients	No. relapses	\(\hat{\theta}_{0.5}\)	\(\hat{\theta}_{0.025}\)	\(\hat{\theta}_{0.975}\)	TPP decision	\(\hat{\psi}_1\)	\(\hat{\psi}_2\)	\(\hat{\psi}_3\)
1	26	30	0						0.000	0.022
2	16	30	1	0.111	-0.129	0.422	Continue	0.808	0.001	0.026
3	16	30	0	0.233	-0.012	0.569	Continue	0.966	0.004	0.240
4	16	30	0	0.319	0.054	0.688	GO	0.991	0.048	0.715
5	16	30	0	0.556	0.257	0.950	GO	1.000	0.947	0.997

Frequentist summaries

P(top regimen has steepest estimated slope)

condition	nk	p.true.present
Even	20	0.914
Even	30	0.968
Even	40	0.981
Even	60	1.000
Even	80	1.000
High	20	0.601
High	30	0.648
High	40	0.661
High	60	0.768
High	80	0.786
High-low	20	0.966
High-low	30	0.994
High-low	40	0.998
High-low	60	1.000
High-low	80	1.000

condition	nk	prop	Regimen
Even	20	0.002	Regimen 1
Even	20	0.011	Regimen 2
Even	20	0.065	Regimen 3
Even	20	0.250	Regimen 4
Even	20	0.672	Regimen 5
Even	30	0.003	Regimen 2
Even	30	0.042	Regimen 3
Even	30	0.202	Regimen 4
Even	30	0.753	Regimen 5
Even	40	0.024	Regimen 3
Even	40	0.183	Regimen 4
Even	40	0.793	Regimen 5
Even	60	0.069	Regimen 4
Even	60	0.931	Regimen 5
Even	80	0.035	Regimen 4
Even	80	0.965	Regimen 5
High	20	0.183	Regimen 2
High	20	0.220	Regimen 3
High	20	0.271	Regimen 4
High	20	0.326	Regimen 5
High	30	0.144	Regimen 2
High	30	0.210	Regimen 3
High	30	0.262	Regimen 4
High	30	0.384	Regimen 5
High	40	0.142	Regimen 2
High	40	0.193	Regimen 3
High	40	0.291	Regimen 4
High	40	0.374	Regimen 5
High	60	0.069	Regimen 2
High	60	0.184	Regimen 3
High	60	0.277	Regimen 4
High	60	0.470	Regimen 5
High	80	0.066	Regimen 2
High	80	0.146	Regimen 3
High	80	0.266	Regimen 4
High	80	0.522	Regimen 5
High-low	20	0.001	Regimen 1
High-low	20	0.009	Regimen 3
High-low	20	0.369	Regimen 4
High-low	20	0.621	Regimen 5
High-low	30	0.003	Regimen 3
High-low	30	0.345	Regimen 4
High-low	30	0.652	Regimen 5
High-low	40	0.347	Regimen 4
High-low	40	0.653	Regimen 5
High-low	60	0.228	Regimen 4
High-low	60	0.772	Regimen 5
High-low	80	0.190	Regimen 4
High-low	80	0.810	Regimen 5

Frequentist summary of estimator performance across changes in sample size (nk) and differences in \(\log_{10}\)(TTP) slope. For all panels, results are based on 1,000 simulated datasets were used for each sample size and condition. A) The proportion of simulations where a given regimen was estimated to have the steepest slope. B) The proportion of simulations where the steepest estimated slope belonged to one of the true top two steepest regimens. C) The proportion of simulations (y-axis) where the estimated control slope falls outside of the estimated 95% confidence interval for a regimen with a given effect size (x-axis).